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Friday, February 1, 2013

Mathematics in 2025

The National Research Council of the National Academies has
just released the preliminary version of its report, The Mathematical Sciences in 2025[1]. This was produced in response to a request from the National
Science Foundation. It comes as the latest in a series of glimpses into the
future of mathematics that go back to the “David reports” of 1984 and 1990 [2,3]
and the “Odom study” of 1998 [4]. This report is important because it will
influence the direction NSF takes as it plans for the future.

The emphasis of the report is on the central role that the
mathematical sciences are taking within research in areas as diverse as
biology, finance, and climate science. Traditional disciplinary boundaries are
blurring. There is an increasing need for scientists who are well grounded in
mathematical sciences, especially the statistical and computational sciences,
as well as other disciplines. This goes two ways. It means opening courses and
programs in the mathematical sciences, especially at the graduate level, to
those in other fields of study, and it means ensuring that students graduating in
the mathematical sciences are prepared to work in this interdisciplinary world.

This has implications right down the line of mathematics
education. The authors of the report question whether, in a scientific world
that is dominated by big data and the challenges of large-scale computation,
the traditional calculus-focused curriculum is the most appropriate for all
students. As they say, “Different pathways are needed for students who may go
on to work in bioinformatics, ecology, medicine, computing, and so on. It is
not enough to rearrange existing courses to create alternative curricula; a redesigned offering of courses and majors
is needed [my emphasis].” (NRC 2013, p. S-9)

The report also stresses the importance of attracting more
women and students from traditionally underrepresented minorities to the mathematical
societies. This is the one place where I disagree with the report, for it
asserts that, “While there has been progress in the last 10–20 years, the
fraction of women and minorities in the mathematical sciences drops with each
step up the career ladder.” (NRC 2013, p. S-10). I don’t question the drop. I
question whether there has been progress over the last 10–20 years.

If we look at mathematics majors (bachelor’s degrees) by
gender, we see that over the period 1990 to 2011 the number of men majoring in
mathematics grew by 25% while the number of women grew by only 10% (Figure 1).
As a result, the percentage of bachelor’s degrees in the mathematical sciences
going to women has dropped to 43.1%, the first time it has been this low since
1981. This is having knock-on effects for graduate programs. The percentage of
bachelor’s degrees in mathematics that went to women peaked in 1999 at 47.8%.
The percentage of master’s degrees in mathematics that went to women peaked in
2004 at 45.1% and has since dropped back to 40.9%. The percentage of doctoral
degrees in mathematics that went to women peaked in 2008 and ’09 at 31.0%. It
has since dropped back to 28.6%. The good news is that the past decade has seen
strong growth in the number of mathematics majors, but two-thirds of the growth
since 2001 has been in the number of men.

We see an even more discouraging pattern among Black students
(Figure 2). The number of Black mathematics majors is essentially back to where
it was twenty years ago despite the number of bachelor’s degrees earned by
Black students almost tripling over this period. The number of Black
mathematics majors peaked in 1997 at 1,089. It was back down to only 840 in
2011. The number of ethnically Asian mathematics majors has been growing
strongly over the past decade. Even so, the number earning undergraduate degrees
in the mathematical sciences has only doubled since 1990, while the number
earning bachelor’s degrees has tripled. The growth in the number of Hispanic
mathematics majors looks good, having slightly more than tripled in twenty
years, until you realize that the number of Hispanic students graduating from
college is almost five times what it was in 1990 (154,000 versus 33,000). Where
we do see strong growth, especially since 2007, is in the number of
non-resident aliens majoring in mathematics, which now stands at 7% of all US
mathematics majors.

I must emphasize that the NRC report does highlight the
importance of increasing the participation of women and members of
underrepresented groups. It includes the following specific recommendation:

Recommendation
5-4:
Every academic department in the mathematical sciences should explicitly
incorporate recruitment and retention of women and underrepresented groups
into the responsibilities of the faculty members in charge of
the undergraduate program, graduate program, and faculty hiring and
promotion. Resources need to be provided to enable departments to adopt,
monitor and adapt successful recruiting and mentoring programs that have
been pioneered at other schools and to find and correct any disincentives
that may exist in the department. (NRC 2013, p. 5-18)

I have only touched on a few of the topics covered in the NRC
report. It also discusses the increasingly important role of the mathematical
sciences institutes, the issue of maintaining online repositories of mathematical
research such as arXive, and the threats to
mathematics departments as more instruction—especially for the service courses
that often provide the justification for a large mathematics faculty—is moved
online. This is a report well worth reading and pondering.